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Sequential Monte Carlo smoothing for general state space hidden Markov models

Abstract : Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and central limit theorems, are established. In particular, time uniform bounds on the marginal smoothing error are obtained under appropriate mixing conditions on the transition kernel of the latent chain. In addition, we propose an algorithm approximating the joint smoothing distribution at a cost that grows only linearly with the number of particles.
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https://hal.archives-ouvertes.fr/hal-00839311
Contributor : Médiathèque Télécom Sudparis & Institut Mines-Télécom Business School <>
Submitted on : Thursday, June 27, 2013 - 4:41:54 PM
Last modification on : Wednesday, October 14, 2020 - 4:10:20 AM

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Randal Douc, Aurélien Garivier, Éric Moulines, Jimmy Olsson. Sequential Monte Carlo smoothing for general state space hidden Markov models. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2011, 21 (6), pp.2109-2145. ⟨10.1214/10-AAP735⟩. ⟨hal-00839311⟩

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